Economic Scenario Reduction

45PD: Model Efficiency

Mary Pat Campbell

Who Should Join?

• Actuaries at the onset of their careers who likely

run models.

• Actuaries who provide opinions based on the

results of models.

• Everyone at this session!

https://www.soa.org/Professional-

Interests/modeling/modeling-detail.aspx

Join the New Modeling Section!

Two Types of Scenario Clustering:

• Type I: Use scenario data directly. Since the location

variables for this type are from scenario data directly,

there is no need to run the model.

• Type II: Use location variable data derived from the

scenarios, such as wealth ratios. This type only need

to run a single cell model.

Revisit: Scenario Clustering

• Single set of scenarios to be used over multiple

lines of business, to be incorporated later

(ORSA, CTE, etc.)

• Comparability between results

• Sensitivity testing non-scenario assumptions

• Only requires the original “full” scenario set,

does not require underlying variates

• Really easy to implement

Why Use Type I Clustering/Selection?

• Stratified Sampling

• Trying to capture entire distribution, at equal

intervals

• Importance Sampling

• Want to “oversample” the more important parts of

the distribution

• Cluster Sampling

• Group scenarios together in “natural” clusters, pick

one from each cluster as representative

Scenario Reduction Approaches

Original Sample: Want 10% Sample

Simplistic: Take Every Tenth Sample

Stratified: Order Samples before Subsampling

Importance: “Oversample” In Specific Parts – Right

Tail

Importance: “Oversample” In Specific Parts –

Extremes (Pivoting)

Cluster Sampling: k-means Sampling

• AIRG: Free ESG at SOA website

• Run info:

• Version used: 7_1_201406

• Starting date: 12/31/2013

• Annual time step

• Only looking at interest rate scenarios

• Structure of interest rate model: two variables in

stochastic difference eqn – 20-yr rate and

difference between 20-yr and 1-yr rate

• Yield curve generated with Nelson-Siegel formula

(floored at 0)

Example Economic Scenario Generator

• For a given set, a “significance measure” is

calculated

• 20-year rate is used for basis of significance

measure

• Scenarios rank-ordered, pick middle of equally-

divided range (equal weight per scenario)

• Subset of size 1000, 500, 200, 50

Stratified Sampling Example: AIRG

Scenario-Picking Tool

Stratified: 10th Percentile, 20-year rate

Stratified: 90th Percentile, 20-year rate

Stratified: Median, 20-year rate

Stratified: 10th Percentile, 7-year rate

Stratified: 90th Percentile, 7-year rate

Stratified: Median, 7-year rate

Stratified: 10th Percentile, 1-year rate

Stratified: 90th Percentile, 1-year rate

Stratified: Median, 1-year rate

• Distance between two separate scenarios, based

off a key rate over time

𝐷 𝑖, 𝑗

=

𝑡=1

𝑇

𝑚=0

𝑡−1

1 +𝑖𝑚2

−212−

𝑚=0

𝑡−1

1 +𝑗𝑚2

−212

2

• Link to significance measure:

Example Scenario Distance Metric

• For each pair of scenario sets, a distance metric is

calculated

• Pick one scenario randomly to be first pivot

• Find scenario with largest distance from first, designate

second pivot

• Repeat until enough scenarios:• Each scenario assigned to closest pivot

• Find scenario that is farthest from its pivot

• Add this to pivot set

• Pivot gets weight of number of scenarios assigned to it

(including self)

Importance Sampling Example: Pivot

Technique

Pivot Cluster Size Distribution

Pivots: 10th Percentile, 20-year rate

Pivots: 90th Percentile, 20-year rate

Pivots: Median, 20-year rate

Pivots: 10th Percentile, 7-year rate

Pivots: 90th Percentile, 7-year rate

Pivots: Median, 7-year rate

Pivots: 10th Percentile, 1-year rate

Pivots: 90th Percentile, 1-year rate

Pivots: Median, 1-year rate

• For each pair of scenario sets, a distance metric is

calculated

• Do k-means clustering technique based on this metric

• Use scenario closest to centroid to represent each

cluster

• This representative scenario weighted by number of

scenarios in the cluster

Clustering Example

Cluster Size Distribution

Cluster Size Distribution

Cluster Size Distribution

Cluster Size Distribution

Cluster: 10th Percentile, 20-year rate

Cluster: 90th Percentile, 20-year rate

Cluster: Median, 20-year rate

Cluster: 10th Percentile, 7-year rate

Cluster: 90th Percentile, 7-year rate

Cluster: Median, 7-year rate

Cluster: 10th Percentile, 1-year rate

Cluster: 90th Percentile, 1-year rate

Cluster: Median, 1-year rate

• Stratified Sampling

• Very easy to implement, easy to explain

• Don’t have to worry about uneven weights

• Importance Sampling – Pivot Procedure

• Use when extremes are most important or most

sensitive in results

• Issue with overly large pivot clusters

• Too few pivots – watch out!

• Clustering – k-means Procedure

• Useful when very few scenarios can be run

General Observations

• Modeling Efficiency Work Group

• http://actuary.org/content/academy%E2%80%99s-model-efficiency-work-

group

• Bibliography:

http://dev.actuary.org/files/Modeling%20Efficiency%20Bibliography%20-

%20Update%2012-11.pdf

• Academy Interest Rate Generator

• Spreadsheet and FAQ: https://www.soa.org/research/software-

tools/research-scenario.aspx

• Release Notes:

http://www.actuary.org/life/zip10/Release_notes_for_version7.pdf

• SOA Research

• Model Efficiency Study Results:

https://www.soa.org/files/research/projects/research-2011-11-model-eff-

report.pdf

Resources